# Solve 2D Math Equations Colorfully

Electronics can be seen as really just an application of physics, and you could in turn argue that physics is the application of math to the real world. Unfortunately, the way most of us were taught math was far from intuitive. Luckily, the Internet is full of amazing texts and videos that can help you get a better understanding for the “why” behind complex math topics. Case in point? [3Blue1Brown] has a video showing how to solve 2D equations using colors. If you watch enough, you’ll realize that the colors are just a clever way to represent vectors and, in fact, the method would apply to complex numbers.

Honestly, we don’t think you’d ever solve equations like this by hand — at least not with the colors. But the intuitive feel this video can give you for how things work is very valuable. In addition, if you were trying to implement an algorithm in software this would be tailor-made for it, although you wouldn’t really use colors there either we suppose.

The video is a bit long, but it is packed full of interesting insights. He shows several ways to represent functions in addition to the color method. Just watching the animations can bring on some “aha” moments. If you are a programmer at heart, you’ll no doubt pick up on the binary search aspect of the algorithm, too.

If you want a refresher on complex numbers, we did that already. If you are into software-defined radio, don’t forget all this would apply to I and Q signals, too.

## 13 thoughts on “Solve 2D Math Equations Colorfully”

1. Ostracus says:

“Electronics can be seen as really just an application of physics, and you could in turn argue that physics is the application of math to the real world. Unfortunately, the way most of us were taught math was far from intuitive. ”

Don’t know if either is always “intuitive”. And yes rote doesn’t help with intuitive either.

2. targetdrone says:

Usually, I like his videos and find them intuitive, but this one doesn’t do it for me. I have a hard time discerning small patches of colors, so the whole concept fails.

1. EndlessYellowParcels says:

Ignore the color part and focus on the winding / search algorithm part. That part was neat.

3. EndlessYellowParcels says:

Oh good, hackaday did already cover the video on Fourier transforms too.

That video is so, so, sooooo good.

4. Nikolai says:

Look like a fat woman scratching her rear.

1. [EGO] says:

You have a very active imagination. Never change.

5. Galane says:

The thumbnail on the video reminds of the videogame, QIX. How about a computer running OpenCV learning how to play and beat QIX?

6. jackcrenshaw says:

Awesome!! I love it!!! But what I really want to know — what burns at my soul — is how these guys produced the awesome, animated videos. I think I heard him mention an app, but it went whizzing past before I got it.

Can anyone help me out here??

1. RP says:

He said in an earlier video that he writes the animations in Python

1. jackcrenshaw says:

Wow! Thanks!

7. David says:

Challener, D. and Rubel, L. “A Converse to Rouché’s Theorem.” is related.

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